Indoor positioning with GNSS encounters several limitations. One is the power of the signal that is too weak indoors. The Assisted-GNSS (A-GNSS) and High sensitivity GNSS (HS-GNSS) are answers to the weak signal problem. They allow decreasing the detection level of the satellite signal down to -150 or -160 dBm which makes signals measurable in "light indoor" environments ("light indoor" corresponds to environments where the signal is not totally absent like the top floor of a building or nearby the windows). However the attenuation of walls and roof can easily overtake 30 dB in very common cases: A-GNSS and HS-GNSS are then inefficient. The GNSS repeater based indoor positioning system, already fully described in previous papers [1], proposes to solve the problem with a low cost infrastructure. This method is based on the use of so-called GNSS repeaters that have the role of collecting the GNSS signals in the best possible environment (namely outdoors on the roof of the building) or from a GNSS signal generator. A local network of antennas is deployed indoors and linked to the signal source (the signal generator or the roof antenna), in order to recreate a local constellation of repeaters whose positions have to be known to the receiver. The signal source is sequentially transmitted in such a way that each antenna broadcasts the signal during a limited period of time. Thus, a cycle of emission is obtained. A full cycle is obtained when all the antennas have broadcasted the signal once. When the first cycle is finished, another one starts, and so on. If we consider a receiver located indoors which is measuring the pseudo-ranges from all the satellites, we observe a jump in the measurements of the pseudo-ranges. Let us consider d1 the distance between the antenna of the Receiver and the antenna of Repeater 1 and d2 the distance between the antenna of the Receiver and the antenna of Repeater 2. Then, if the cables from the source to the antennas of the repeaters have the same length, this jump corresponds to the difference d2-d1. At the end of a cycle (with a network of 4 repeaters) we have enough measurements to calculate a 3D position. This is a very low cost infrastructure solution for indoor positioning since the electronics managing the sequence of emission is very simple. However, the Repeater technique does not solve the problem of the presence of strong short multipath that limits the accuracy of the pseudo-range measurements, and consequently the differences of pseudo-ranges. Multipath error is difficult to predict and changes in space and over time [2]. For this reason, there are no really accurate models for multipath indoors. Nevertheless, many techniques were developed to reduce the effect of multipath on code measurements. These techniques improve considerably the synchronization error, especially in the case of medium and long multipath. However, for short multipath, the error remains substantial. In addition, for indoor positioning where an accuracy of a few meters is required, these techniques are not sufficient. Considering the GPS L1 civil signal, our definition of short multipath is the ones having a delay length inferior to 146.5 m (half a chip of code). Thus we can consider that indoor applications using repeaters mainly involve only short multipath which is generated after reflections on nearby objects, as shown in [2]. The main goal is to find a way to remove short delay multipath effect on code measurements in order to improve the accuracy of pseudo-range difference measurements in the very specific context of the repeater based technique. A specific tracking loop discriminator (the so-called SMICL) which is able to mitigate the short multipath was developed to fulfill the goal. The theoretical description and validation of the new loop discriminator are available in [3] and [4] respectively.